Question

Area of rhombus is 96cm”, one diagonal is 16cm, find its other diagonal.​

Answer 1

Given : Area of rhombus is 96cm². One diagonal is 16cm.

To Find : Other diagonal of the rhombus.

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Here, area of the rhombus is given as 96cm² and one diagonal is given as 16cm. So, let the first diagonal be d1 and second diagonal be d2. And now we'll apply the formula for the area of the rhombus.

$\: \:$

As we know that :

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$\star \: \underline{\boxed{\mathfrak\purple{Area \: of \: the \: rhombus \: = \frac{1}{2} \times d_{1} \times d_{2}}}}$

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$\: \:$

Now, we'll put the values of area as well as first diagonal in the formula.

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$\sf:\implies \: Area_{(rhombus)} = \dfrac{1}{2} \times d_{1} \times d_{2} \\ \\ \\ \sf:\implies \: 96 = \frac{1}{2} \times 16 \times d_{2} \\ \\ \\ \sf:\implies \: d_{2} = \frac{{\cancel96 }\times 2}{\cancel{16}} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{d_{2} = 12cm}}} \: \bigstar \: \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: second \: diagonal \: of \: the \: rhombus \: is \: \bold{12 \: cm}.}}$

Answer 2

Given:

• Area of rhombus = 96 cm²

• Length of one of it's diagonal = 16 cm

To find:

• Length of another diagonal.

Solution:

» Area of rhombus = ½ × D1 × D2

» 96 = ½ × 16 × D2

» D2 = 12 cm

Therefore, the length of the another diagonal is 12 cm.